CS162 Week 8 Kyle Dewey

Overview Example online going over fail03.not (from the test suite) in depth A type system for secure information flow Implementing said type system

Flashback: Assignment 2 Implemented dynamically enforced secure information flow via label tracking Each Storable is labeled with a tag describing its security level Security levels interact in well-defined ways

Security Levels Publi c Secr et AliceBob Most Secure Least Secure ⊑ ⊑ ⊑ ⊑ Most Precise Least Precise

Basic Idea Specify which channel we output to (public, secure, etc.) Only output values of equal or lesser security than the specified value (i.e. do not output something secure on a public channel) When values interact to produce new values, the new values take the security level of the most secure thing they touched

Example var x, y inoutput secret "enter secret number: ";x := input secret num;y := x;output public y

Issues This system works, but there are two major issues with it (well, 1.5 major issues) What’s problematic?

#1: Termination Leaks Whether or not a program halts can leak a bit to an attacker In a dynamic system, certain kinds of leaks are transformed into termination leaks I.e. instead of outputting a secret value to public, throw an exception and terminate instead

#2: Dynamic var x, y in x := input secret num; y := input public num; if (y = 42) { output public x }

A Solution A static type system and type checker, specifically for secure information flow If a program typechecks, then it is guaranteed that it is secure Type systems being type systems, if it does not typecheck, it still might be secure

Assignment 5 Implement a type checker for secure information flow for miniJS Same syntax from assignment 2 Implicitly typed The type system, along with all the necessary rules, is provided Overall very similar to the type system coverage in the lecture

Major Difference from Lecture Lecture is using equivalence constraints Solved using the union-find data structure This assignment will use subset constraints These slides cover how to solve these

Three Core Challenges 1. Understanding the math 2. Implementing the math 3. Solving the constraints

#1 Understanding The Math Basics needed to understand it covered extensively in lecture Biggest difference from lecture: L is used as a type variable instead of T, since L is a security level

#2 Implementing Math General rule: implement as close to the math as possible The more it deviates, the more difficult it is to reason about whether or not they are equivalent...and the more difficult it becomes to track down bugs

Implementing Math

#3: Solving the Constraints

Constraint Generation Very similar to how constraints were generated in lecture Based on subsets instead of equality

Constraint Generation Once all the rules have completed, we end up with a bunch of constraints like these: Public ⊑ L ₁ Public ⊑ L ₂ Public ⊑ SecretPublic ⊑ L ₃ L ₃ ⊑ L ₁ L ₂ ⊑ L ₄ Secret ⊑ L ₄...where L ₁, L ₂, and L ₃ are type variables

Constraint Meaning These constraints show what the syntax of the program says about the security lattice We already know what the security lattice looks like If the two are consistent, the program typechecks If there are inconsistencies, the program fails to typecheck

Finding Inconsistencies Publi c Secr et AliceBob ⊑ ⊑ ⊑ ⊑ If any constraints violate this partial order, it means the program is not well-typed Secret ⊑ Public Secret ⊑ Bob Secret ⊑ Alice Bob ⊑ Public Alice ⊑ Public Bob ⊑ Alice Alice ⊑ Bob

Not that Easy What about type variables? Need a way to map these back to concrete types Public ⊑ L ₁ Public ⊑ L ₂ Public ⊑ SecretPublic ⊑ L ₃ L ₃ ⊑ L ₁ L ₂ ⊑ L ₄ Secret ⊑ L ₄

Coalescing Constraints Public ⊑ L ₁ Public ⊑ L ₂ Public ⊑ SecretPublic ⊑ L ₃ L ₃ ⊑ L ₁ L ₂ ⊑ L ₄ Secret ⊑ L ₄ Publi c Secr et L₁L₁L₁L₁ L₂L₂L₂L₂ L₃L₃L₃L₃ L₄L₄L₄L₄ Edges denote ⊑

Getting the Full ⊑ Publi c Secr et L₁L₁L₁L₁ L₂L₂L₂L₂ L₃L₃L₃L₃ L₄L₄L₄L₄ If node n 1 can reach node n 2, then n 1 ⊑ n 2 Public ⊑ : {L ₁, L ₂, L ₃, L ₄, Secret} Secret ⊑ : {L ₄ }

Cycles The graph can contain cycles This should not break anything Publi c Secr et L₁L₁L₁L₁ L₂L₂L₂L₂ Public ⊑ : {L ₁, L ₂ } Secret ⊑ : {L ₁, L ₂ }

Final Step Verify the full sets are consistent Only need to consider concrete security levels (public, secure, etc.) Secret ⊑ Public Secret ⊑ Bob Secret ⊑ Alice Bob ⊑ Public Alice ⊑ Public Bob ⊑ Alice Alice ⊑ Bob Secret cannot reach Public Secret cannot reach Bob Secret cannot reach Alice Bob cannot reach Public Alice cannot reach Public Bob cannot reach Alice Alice cannot reach Bob

Constraint Solver Implementation Free to use mutability It is not necessary to make an explicit graph, but you are free to do so if you wish It is likely easier to avoid it if possible For each constraint, add an edge and possibly nodes to this graph A global counter will be needed for generating unique type variables

Removed for Simplicity Each node should have an edge pointing to itself Since the definition of ⊑ includes equality, for all levels l, l ⊑ l Hint: this can be exploited in implementations that do not have an explicit graph

The Math in Depth

fail03.not Example